But too bad that if you then use that path as a Clipping Mask the rounding effect will break. And if you do the Clipping Mask first, then try to add the Round Corners effect the image disappears. If trying to use this method with a Clipping Mask you can't win.
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MentalistMay 17 at 7:55

Seems you've already figured out that the Stylize Effect is a better method. If you want to go one step further check out VectorScribe from http://www.astutegraphics.com it's a fabulous plug in that will allow you to not only continually round any corner but also had many other very useful features.